
where \(a=\sum _{w\in \Sigma ^{\textrm {\tiny (2)}}} \, a_w\) .
This partition function is independent of the chosen cell decomposition of
\(\Sigma \)  [1]} and hence agrees with its continuum limit where the lattice
discretisation becomes finer and finer:
the heat kernel defines a
renormalisation group-invariant amplitude on the faces so that the
partition function is invariant under subdivision of the lattice. This
feature is special to Yang-Mills theory in two dimensions, and
for this reason the lattice regularisation of the quantum gauge theory actually computes
the partition function (REF ) exactly (up to
the undetermined constants \(\upsilon _1\)  and \(\upsilon _2\) ).
